Dynamics, circuit implementation and synchronization of a new three-dimensional fractional-order chaotic system

2017 ◽  
Vol 82 ◽  
pp. 435-445 ◽  
Author(s):  
Xu Zhang ◽  
Zhijun Li ◽  
De Chang
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Circuit Implementation

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

Dynamics analysis and circuit implementation of a new three-dimensional chaotic system

Optik ◽  
2015 ◽  
Vol 126 (7-8) ◽  
pp. 765-768 ◽  
Author(s):  
Wu-jie Zhou ◽  
Zhong-peng Wang ◽  
Ming-wei Wu ◽  
Wei-hong Zheng ◽  
Jian-feng Weng
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Dynamics Analysis ◽  
Circuit Implementation

scholarly journals Analysis, circuit implementation and synchronization of a new three-dimensional chaotic system

2006 ◽  
Vol 55 (8) ◽  
pp. 4005
Author(s):  
Wang Fan-Zhen ◽  
Qi Guo-Yuan ◽  
Chen Zeng-Qiang ◽  
Zhang Yu-Hui ◽  
Yuan Zhu-Zhi
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Circuit Implementation

A Novel Cubic–Equilibrium Chaotic System with Coexisting Hidden Attractors: Analysis, and Circuit Implementation

2017 ◽  
Vol 27 (04) ◽  
pp. 1850066 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
Autonomous System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Dynamical Properties

Chaotic systems with a curve of equilibria have attracted considerable interest in theoretical researches and engineering applications because they are categorized as systems with hidden attractors. In this paper, we introduce a new three-dimensional autonomous system with cubic equilibrium. Fundamental dynamical properties and complex dynamics of the system have been investigated. Of particular interest is the coexistence of chaotic attractors in the proposed system. Furthermore, we have designed and implemented an electronic circuit to verify the feasibility of such a system with cubic equilibrium.

A Novel 3D Fractional-Order Chaotic System with Multifarious Coexisting Attractors

2019 ◽  
Vol 29 (01) ◽  
pp. 1950004 ◽  
Author(s):  
Chengyi Zhou ◽  
Zhijun Li ◽  
Yicheng Zeng ◽  
Sen Zhang
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Order System ◽  
Attractive Feature ◽  
Huge Amount ◽  
Coexisting Attractors ◽  
Interesting Phenomenon ◽  
Periodic Attractors

A novel three-dimensional fractional-order autonomous chaotic system marked by the ample and complex coexisting attractors is presented. There are a total of seven terms including four nonlinearities in the new system. The evolution of coexisting attractors of the system are numerically investigated by considering both the fractional-order and other system parameters as bifurcation parameters. Numerical simulation results indicate that the system has a huge amount of multifarious coexisting strange attractors for various ranges of parameters, including coexisting point, periodic attractors, multifarious coexisting chaotic, and periodic attractors. Compared with other chaotic systems, the biggest difference and most attractive feature is the capability of the proposed fractional-order system to produce coexisting attractors that undergo a simultaneous displacement phenomenon with variation of a single parameter. Moreover, it is worth noting that constant Lyapunov exponents and the interesting phenomenon of transient coexisting attractors are also observed. Finally, the corresponding implementation circuit is designed. The consistency of the hardware experimental results with numerical simulations verifies the feasibility of the new fractional-order chaotic system.

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